Conductance Phases in Aharonov-Bohm Ring Quantum Dots

TL;DR

This paper explains conductance phase regimes in quantum dot Aharonov-Bohm rings using a Green function approach, linking physical dissipation and Fano-like levels to observed phase transitions.

Contribution

It introduces a Green function formalism that accounts for conductance phase regimes in quantum dots with an equi-spaced ladder of electronic levels, incorporating dissipation and meta-stable states.

Findings

Identification of growing and self-returning phase regimes in conductance.

Linking dissipation rate to phonon coupling.

Mathematical description of phase transition via complex transmission zeros.

Abstract

The regimes of growing phases (for electron numbers N~0-8) that pass into regions of self-returning phases (for N>8), found recently in quantum dot conductances by the Weizmann group are accounted for by an elementary Green function formalism, appropriate to an equi-spaced ladder structure (with at least three rungs) of electronic levels in the quantum dot. The key features of the theory are physically a dissipation rate that increases linearly with the level number (and tentatively linked to coupling to longitudinal optical phonons) and a set of Fano-like meta-stable levels, which disturb the unitarity, and mathematically the change over of the position of the complex transmission amplitude-zeros from the upper-half in the complex gap-voltage plane to the lower half of that plane. The two regimes are identified with (respectively) the Blaschke-term and the Kramers-Kronig integral term in the theory of complex variables.